U.S. patent number 4,315,263 [Application Number 06/076,695] was granted by the patent office on 1982-02-09 for navigational systems using phase encoded angular coordinates.
Invention is credited to Norman S. Neidell.
United States Patent |
4,315,263 |
Neidell |
February 9, 1982 |
Navigational systems using phase encoded angular coordinates
Abstract
This invention generally relates to navigation systems which
seek to position in real time with appropriate accuracy one or more
mobile platforms in reference to a known system of coordinates by
the emission of signals into a propagation medium and processing
them after detection. Broad-band, broad-beam signals are employed.
All received signals convey phase encoded angular coordinate
information which characterizes the particular signal path. When
the angular coordinate information is used in conjunction with
range determinations from detected signals, an especially useful
navigation system is provided which can operate using only a single
reference station.
Inventors: |
Neidell; Norman S. (Houston,
TX) |
Family
ID: |
27560807 |
Appl.
No.: |
06/076,695 |
Filed: |
September 18, 1979 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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925903 |
Jul 19, 1978 |
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691674 |
Jun 1, 1976 |
4114153 |
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483202 |
Jun 26, 1974 |
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Current U.S.
Class: |
342/451;
342/378 |
Current CPC
Class: |
G01S
3/80 (20130101); G01S 7/292 (20130101); G01S
7/41 (20130101); G01S 7/527 (20130101); G01S
13/02 (20130101); G01S 15/582 (20130101); G01S
13/28 (20130101); G01S 13/30 (20130101); G01S
13/42 (20130101); G01S 13/878 (20130101); G01S
15/108 (20130101); G01S 13/106 (20130101) |
Current International
Class: |
G01S
13/00 (20060101); G01S 7/02 (20060101); G01S
7/527 (20060101); G01S 7/523 (20060101); G01S
3/00 (20060101); G01S 13/87 (20060101); G01S
3/80 (20060101); G01S 13/02 (20060101); G01S
15/00 (20060101); G01S 15/58 (20060101); G01S
13/28 (20060101); G01S 13/42 (20060101); G01S
7/41 (20060101); G01S 13/30 (20060101); G01S
15/10 (20060101); G01S 13/10 (20060101); G01S
7/292 (20060101); G01S 003/02 () |
Field of
Search: |
;343/1CL,9R,112C,112R
;367/90,100 |
References Cited
[Referenced By]
U.S. Patent Documents
Primary Examiner: Blum; Theodore M.
Attorney, Agent or Firm: Pravel, Gambrell, Hewitt, Kirk,
Kimball & Dodge
Parent Case Text
REFERENCE TO RELATED APPLICATION
This application is a continuation of co-pending U.S. Patent
Application Ser. No. 925,903, filed July 19, 1978 which is a
continuation-in-part of my copending U.S. Patent Application Ser.
No. 691,674, filed June 6, 1976 now U.S. Pat. No. 4,114,153, dated
Sept. 12, 1978 which in turn is a continuation of prior co-pending
U.S. Patent Application Ser. No. 483,202 filed June 26, 1974 and
now abandoned.
Claims
What is claimed is:
1. In a method of ascertaining for at least one mobile unit,
navigational information in terms of at least one angular
coordinate, radial ranges, and relative velocity components, by
transmitting from at least one transmitter and receiving with at
least on receiver, at least one component signal in a medium of
known propagation velocity, characterized by:
forming each said component signal to consist of at least one
member signal, all said component signals being separable;
phase encoding in at least one said member signal a distinction in
phase according to at least one angular coordinate;
receiving said component signals, separating them, and identifying
within each said component signal each individual member
signal;
measuring phases for each one of said identified member
signals;
decoding each said angular coordinate from said measured phases and
said encodings produced by said encoding step;
measuring signal transit times for any member signal having a known
time of initiation;
measuring interval times between member signals for any member
signals whose interval time is initially known;
forming corrected measured signal transit times and interval times
by compensating each so formed time for any linear elements in said
phase encodings;
producing mobile unit relative velocity components from any said
corrected measured interval times;
producing mobile unit radial ranges from any corrected signal
transit times, and
correcting any said radial ranges for any known relative velocity
components.
2. The method of claim 1 characterized in that a phase distortion
produced by properties of the signal propagation medium is present
in each member signal, the medium phase distortion being
independent of all other phase encodings, the number of independent
encodings being at least equal to one more than said number of
angular coordinates, and
obtaining said medium phase distortions from said measured phases
and said known phase encodings.
3. The method of claim 1 characterized in that for at least one
mobile unit which has established its location from said
navigational, reflected component signals from other mobile units
are used to establish their positions in relation to said mobile
unit of established location.
4. The method according to claim 1 characterized in that phases are
measured for identified member signal phase spectra.
5. The method of claim 1 characterized in that said angular
coordinate is encoded as a phase distortion introduced by
propagating the transmitted component signal through a medium
having dispersive properties which vary in relation to the angular
coordinate.
6. The method of claim 1 characterized in that said angular
coordinate is encoded as a phase distortion introduced by
reflecting the transmitted component signal from a surface
positioned beyond the critical angle in relation to the angular
coordinate.
7. The method according to claim 1 characterized in that each
component signal has defined polarization character, the member
signals of each component signal being formed as a weighted sum of
a design base signal pair, a pair of base signals substantially
being in quadrature and sharing a common smooth and essentially
unimodal amplitude spectrum occupying a contiguous band of
frequencies,
choosing design base signal pairs for each component signal such
that component signals are separable by the logical sum of an
distinction in polarization character, frequency content and member
signal pattern,
separating received component signals and forming replicas for
processing,
processing said replicas by cross-correlating with detection base
signal pairs, thereby producing a pair of correlation component
functions for each component signal, said detection base signal
pairs having properties analogous to said design base signal pairs,
but with counterpart design and detection base signal pairs
overlapping in frequency by a band greater in width than any
frequency shift attributable to mobile unit relative motions, the
difference in phase angle at any common frequency being
substantially a constant and a complementary second constant
multiplying the frequency,
forming for each received component signal a correlation amplitude
function from term-by-term sums of the absolute values of the
correlation component function pairs, said absolute values being
raised to a like power not less than one and raising said sums to a
power greater than zero but less than one, and
identifying from the maxima of the correlation amplitude function
individual member signals.
8. The method according to claim 7 characterized in that for at
least one component signal a single angular coordinate is encoded
as a phase distortion which is substantially a constant and a
complementary second constant multiplying the frequency;
developing member signals for said component signals and processing
said component signals using design and detection base signal
pulses, individual base signal pulses having the further property
that the phases at all significant frequencies are substantially a
constant and a complementary second constant multiplying the
frequency;
measuring the constant phases of individual member signals in said
received and processed component signals;
correcting said measured constant phases for the constant phase
values of the base signal pulses;
decoding said angular coordinates from said corrected constant
phases, and
forming further corrected signal transit times and interval times
for member signals of said component signals by compensating said
times for any linear phase elements of the base signal pulses as
given by the complementary second constants.
9. The method according to claim 8 characterized in that said
constant phases are measured from identified member signal phase
spectra.
10. The method of claim 8 characterized in that said angular
coordinate is encoded as a phase distortion introduced by
propagating the transmitted component signal through a medium whose
dispersive properties vary in relation to the angular
coordinate.
11. The method of claim 8 characterized in that said angular
coordinate is encoded as a phase distortion introduced by
reflecting the transmitted component signal from a surface
positioned beyond the critical angle in relation to the angular
coordinate.
12. The method according to claim 8 characterized in that the
constant terms of the phase encodings are measured from arctangent
functions of ratios formed from values of identified member signals
at times corresponding to maxima of the correlation amplitude
function, any pair of said values being appropriate to forming a
ratio when the corresponding member signals travel the same path
and are in quadrature.
13. The method of claim 8 characterized in that at least one
component signal consists of more than one member signal, and more
than one angular coordinate is encoded in said component signal,
each phase encoding being substantially a constant and a
complementary second constant multiplying the frequency, so that
for at least one said angular coordinate the encoding is distinct
for at least one member signal, said encodings being independent
and being at least equal in number to the number of angular
coordinates, and
obtaining said angular coordinates from said measured phases and
said phase encodings.
14. The method of claim 8 characterized in that a phase distortion
produced by properties of the signal propagation medium is present
in each member signal, the medium phase distortion being
independent of all other phase encodings, the number of independent
encodings now being at least equal to one more than said number of
angular coordinates, and
obtaining also said medium phase distortions from said measured
constant phases and said phase encodings.
15. The method of claim 13 characterized in that a phase distortion
produced by properties of the signal propagation medium is present
in each member signal, the medium phase distortion being
independent of all other phase encodings, the number of independent
encodings being at least equal to one more than said number of
angular coordinates, and
obtaining also said medium phase distortions from said measured
constant phases and said phase encodings.
16. The method of claim 8 characterized in that for at least one
mobile unit which has established its location from said
navigational information, reflected component signals from other
mobile units are used to establish their positions in relation to
said mobile unit of established location.
17. The method of claim 13 characterized in that for at least one
mobile unit which has established its location from said
navigational information, reflected component signals from other
mobile units are used to establish their positions in relation to
said mobile unit of established location.
18. In a method of ascertaining for at least one mobile unit,
navigational information in terms of at least one angular
coordinate by transmitting from at least one transmitter and
receiving with at least one receiver, at least one component
signal, characterized by:
(1) forming each component signal to include at least one member
signal, all such component signals being separable;
(2) phase encoding, during travel between the at least one
transmitter and at least one receiver, a distinction in phase in at
least one member signal according to at least one angular
coordinate;
(3) receiving the component signals, separating them, and
identifying within each component signal each individual member
signal;
(4) measuring phases for each one of the identified member
signals,
(5) decoding each angular coordinate from the measured phases and
the encodings produced by said step of phase encoding; and
(6) ascertaining the navigational information from each decoded
angular coordinate.
Description
BACKGROUND OF THE INVENTION
According to Karwarth in the Journal of the Institute of
Navigation, Vol. 24, No. 1, pp. 105-120, Jan. 1, 1971, the basic
objective of area navigation is to position in real time with
appropriate accuracy one or more mobile units with reference to
some known coordinate system. The number of coordinates needed
depends upon whether the course of the mobile unit can be charted
on a known surface or must be described in three-dimensional space
as in the respective cases of a ship at sea and an aircraft. The
ability to chart a course based on past, present and future desired
positions is a principal element in distinguishing an area
navigation system from navigation using point-to-point or "homing"
approaches such as VOR/DME (VHF Omnidirectional Range/Distance
Measuring Equipment).
Positions are established in all cases by signal transmission
between the mobile units and at least one transmitter of known
location. The transmissions can be electromagnetic (including
optical) or acoustic in any medium including air. Two basic methods
are normally used to obtain positions:
Positions may be determined from a sufficient number of range
measurements to known reference locations by using what is commonly
known as "range-range" systems, or positions may be determined from
a sufficient number of range differences to known reference
locations, by using what is commonly known as "hyperbolic" systems.
In each case a sufficient number is at least equal to the number of
coordinate values needed.
Direct ranging involves calculation of intersections of the circles
or spheres of uniform range from each reference location to the
mobile unit. By contrast, the locus of equal range difference from
the mobile unit to a pair of reference locations are hyperbolae or
hyperbolae of revolution. Again, positions are calculated by
intersection of curves or surfaces, but in this case related to
hyperbolae, hence the name hyperbolic systems.
An exemplary task of area navigation might be the positioning of a
ship at near shore distances. In range-range operation only two
shore stations are needed while a hyperbolic system requires three.
Three shore stations admit calculation of three range differences
hence providing some element of data redundancy. As a general rule,
hyperbolic systems offset a disadvantage in requiring one more
known reference location than the simplest operable ranging system
by having some degree of data redundancy.
As for the transmitted signals, a variety of differing modes of
operation are possible. Ranges can be determined from signal
transmission time between the mobile unit and a reference location
if the signal initiation time is known, a time standard is
available, and a signal propagation velocity is also known. The
simplest means for establishing known initiation times is to
transmit signals only in response to some interrogation.
Alternatively, if transmissions are synchronized to occur at
regular time intervals, time differences are readily determined
with no interrogation step needed using only a local time standard
and a propagation velocity.
Again, signal transmissions themselves can consist of continuous
waveforms (typically sinusoids), intervals of continuous signal
transmissions, or sequences of pulses. The choice of transmitted
signal reflects consideration of the information desired, mode of
operation (range-range versus hyperbolic), noise effects, and the
extent of Doppler distortions amongst other factors.
Continuous waveforms are the most robust signals in the presence of
noise backgrounds since correlation-type receivers may take
advantage of the extreme signal duration. Such signals have no
resolution in time and are used principally with hyperbolic systems
to establish time-differences by making phase comparisons with
reference signals. Where the transmitter-receiver relative velocity
is not insignificant in proportion to the signal propagation
velocity, Doppler effects shift the frequencies of continuous
waveforms. Frequency shifts may be viewed as errors since they
distort subsequent correlation steps and thus degrade phase
comparisons, however, if such shifts are measured, they do relate
to velocity information should this be desired.
Use of continuous signals over intervals provides time resolution
as well as opportunities for correlation detection, but over
shorter data windows. Again, any Doppler effects may be viewed
either as constituting an error in range determination or if
measured, velocity information. The tolerance of such signals to
noise effects is of course diminished in direct proportion to their
shortened duration.
In the limit, as duration is shortened, pulsed signals must be
considered which when taken individually offer no opportunity to
measure Doppler effects. Hence significant transmitter-receiver
relative velocities will be noted as range errors for such systems.
These signals are also most affected by the presence of noise, but
afford the greatest resolution in making a direct time
measurement.
It follows that the alternative methods of operations which exist
constitute attempts at optimizing a number of trade-offs which
interact with some complexity. The hardware requirements, operation
costs, efficiencies and effectiveness in terms of achievable
accuracy are all essential ingredients which play roles in the
optimization.
The following Table presents a sampling of a number of commercially
available area navigation systems. A much more detailed and
comprehensive tabulation of short and medium range electromagnetic
position fixing systems was presented by Rear Admiral C. Munson at
the XV Annual Congress of Surveyors, Stockholm, June 1977. The
variety of candidate systems gives insight into the way in which
the optimization problem has been addressed. Navigation systems
based on the present invention may serve as replacements for each
of the systems noted in the following table amongst others.
TABLE ______________________________________ OF REPRESENTATIVE
COMMERCIAL AREA NAVIGATION SYSTEMS Operating System and Mode and
Range Company Model Environment Frequency (nm.)
______________________________________ Alpine SUNS 3 transponders-
11 khz. trans- 6 Geo- (Sonic underwater ducer 13, 14, physical
Under- ranging 15 khz. trans- Assoc. Inc. water ponders. Norwood,
Navigation N.J. system) Model 775 Cubic Cor- Autotape Interrogator
2900-3100 93 poration Model and 2 re- mhz. San Diego, DM-40
sponders - Ca. (Electronic surface ranging Positioning system)
Decca Pulse/8 Receiver and 3 100 khz. 300+ Survey or more trans-
Systems mitters - hyper- Inc. bolic or ranging Houston, Tx. Long
Receiver and 2 300-400 mhz. 200+ Range or more trans- Shoran
mitters - surface ranging Hi-Fix/6 Receiver and 2 1.6-5.0 mhz. 100+
or more trans- mitters - hyper- bolic or ranging Sea-Fix Receiver
and 2 2 mhz. <100 or more trans- mitters - hyper- bolic or
ranging Trisponder Mobile station Microwave <50 and at least two
(X Band). remotes - 9350 mhz. surface ranging. (mobile) 9450 mhz.
(remote) Aquafix Surface trans- 10.5-16 khz. <1 mitter with
bottom trans- ponders or hydrophone with radio link - slant ranging
del Norte Trisponder Mobile master Microwave <50 Tech- Model
202a and two slaves - (X Band) with nology, surface ranging 9450
mhz exten- Inc. sion to Euless, Tx. <150 Motorola, RPS
Receiver/Trans- Microwave 50 Scottsdale, (Range mitter and two (X
Band) exten- Arizona Positioning or more Radar 9300-9500 sion to
System) transponders - mhz. 100 surface ranging Mini-
Receiver/Trans- Microwave <20 Ranger mitter and two (X Band)
exten- III System or more Radar 5450-5600 sion to transponders -
mhz. <100 surface ranging Ocean Transnav Transducer and 7.5 (on
approx. Research 6000 four trans- board) or 12 Equipment, Acoustic
ponders - 8.57 (sub- Inc. Navigation surface and marine)khz
Falmouth, System under-water transducer Mass. ranging 10.75, 11.25,
12.25 khz transponders Teledyne Raydist-76 Mobile station 1600-4000
khz approx. Hastings- System and and two or 200 Raydist, DRS-H
three shore sta- day- Hampton, System tions - ranging time Va. and
hyperbolic approx. (for 3rd station) 120 night- time.
______________________________________
SUMMARY OF THE INVENTION
This invention relates to navigation systems which employ phase
encoded angular coordinate information in transmitted signals. The
technology for this invention can conveniently employ the methods
described in my above-referenced patent, which is incorporated
herein by reference.
Component signal trains of member signals convey all of the
navigational information. The component signals which may be
concurrently propagating are always separable and distinguishable
from one another by some combination of frequency content,
polarization character, and member signal pattern. Member signals
are required to have four basic properties.
Broad beam transmitters produce the component signals which
illuminate the navigation area. Broad beam receivers detect these
signals. Angular coordinate information is phase encoded in member
signals by reflective or transmissive mechanisms. All encodings can
be substantially characterized by a phase distortion consisting of
a constant and a second complementary constant which multiplies the
frequency. This approximation produces the first two terms of a
Taylor series developed over frequency, the independent
variable.
Angular coordinates are referred either to receiver or transmitter
locations, and either the receiver or the transmitter can
constitute the known location, depending on the particular
embodiment. Component signal transmissions can be sent in response
to interrogation, at regular time intervals or at random, depending
on the selected mode of operation. In all cases the angular
coordinate information will be conveyed.
Processing the received component signals to identify member
signals may be described by a phase-invariant quadrature
matched-filtering operation which is described in my referenced
patent. Member signal basic properties and such processing of the
received component signals are complementary in that frequency
shifts resulting from relative motion between the transmitter and
receiver do not affect arrival time measurements nor the phase
encoded angular coordinate information.
Relative velocity component information between mobile units and
the known location and radial range information may also be
conveyed by the component signals. Such determinations are possible
if the initial interval time between member signals, the time of
member signal transmission, the signal propagation velocity, and a
time standard are known. Having both range and angular coordinate
information allows development of a navigation system which can
operate using only a single base station.
Since utilization of phase information is the essence of the
invention, several corrections to compensate for phase distortions
are included. Distortions accompanying member signal design and
entering during processing are some which fall in this
category.
The broad beam nature of the transmitters used in this invention
suggests lower signal energy levels than might be achieved with a
narrow beam system. Rapid repetition of these broad beam signals
can however overcome this deficit. Further, the ability to impart
angular coordinate information offers opportunities to overcome the
ambiguities of skywave reflections in electromagnetic embodiments
and multipath reflections in sonar applications.
Advanced embodiments of the invention can allow initial mobile
units to position other mobile units with respect to themselves
once the units have established their locations. The initial mobile
units accomplish this function by using echoes or reflections from
the other mobile units and function in this case as an
echo-location system which is described in my referenced
patent.
Finally, by encoding sufficient redundancy in the member signals,
any phase distortions imparted by the propagation medium may be
measured as a part of the decoding operation. This feature adds
significantly to the robustness of the method of this invention.
Such distortions are illustrated with previously unpublished
results. The phase distortion for sound waves caused by propagation
in water for frequencies in the vicinity of 1.2 mhz is
characterized as a function of the propagation path length by the
methods of this invention.
BRIEF DESCRIPTION OF THE DRAWINGS
FIG. 1 shows the time and frequency domain properties of a design
base signal pair having respectively odd and even symmetry;
FIG. 2 shows a generalized embodiment of the invention having a
single transmitter and receiver;
FIG. 3 shows a processing sequence for the embodiment of FIG.
2;
FIG. 4 shows the operations of the navigational information
estimator of FIG. 3;
FIG. 5 shows an elementary electromagnetic area navigation system
having a single base station;
FIG. 6 shows binary encoded member signals at known intervals for
establishing time references;
FIG. 7 shows an experimental apparatus used to characterize the
phase distortion caused by the dispersive properties of water at
1.2 mhz;
FIGS. 8 and 8a shows digitized received member signals for the
apparatus of FIG. 7, after transmission through water, and their
frequency analyses; and
FIG. 9 shows experimental results indicating the relationship of
the phase distortion of member signals at 1.2 mhz with their
propagation distance through water.
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 shows a pair of base signals from which a member signal may
be designed. A single member signal is formed as a linear
combination of a pair of base signals as defined in my
above-referenced patent. In mathematical terms we shall call this
signal
where m and n are constants obeying the relationship m.sup.2
+n.sup.2 =1, and f.sub.o (t), f.sub.1 (t) represent the base
signals.
The four requisite properties I-IV of the base signals f.sub.o (t)
and f.sub.1 (t) are:
I. f.sub.o (t) and f.sub.1 (t) share the common amplitude spectrum
F(w) which is substantially flat or smoothly unimodal over both its
continuous bands at positive and negative frequencies and is
essentially zero elsewhere.
II. There is a finite time interval of duration .alpha., before and
after which both f.sub.o (t) and f.sub.1 (t) may be considered to
be zero, or f.sub.o (t) and f.sub.1 (t) are pulses.
III. f.sub.o (t) and f.sub.1 (t) are in quadrature or constitute a
Hilbert transform pair. In other words, at each common frequency
component the signals differ in phase by 90.degree..
IV. f.sub.o (t) and f.sub.1 (t) must be transformable to odd and
even functions respectively about t=o, defined as the central
coordinate value in their interval of definition of duration
.alpha., by a constant phase shift applied to all frequencies.
Signals termed Klauder signals and Gabor signals described in my
above-referenced patent are in fact two representative types of
signals appropriate for use as the base signals f.sub.o (t) and
f.sub.1 (t). Mathematically these two signal types are defined as:
##EQU1##
Returning now to FIG. 1 (which corresponds to FIG. 12 of my
referenced patent), it shows a diagram of the time domain and
Fourier frequency domain properties of the Klauder base signal pair
termed f.sub.o (t), f.sub.1 (t) (refer to Equation (2A)) which
illustrate the four requisite properties (I through IV) for base
signals.
FIG. 2 shows a generalized embodiment of the invention which
employs a single transmitter 1 and receiver 3. The transmitter 1
produces at least one component signal 1A. A component signal is a
train of member signals which is always separable and
distinguishable from other component signals by some combination of
frequency content, polarization character and member signal
pattern. In cases such as for sonar signals where the polarization
character is alike for all signals, the polarization character
drops out as a possible distinguishing feature. A discussion on
polarization character or state is presented by A. S. Marathay in
Optical Engineering, Vol. 15, No. 4, p. SR 80-81, July-August,
1976.
For the navigation system of FIG. 2, it is required that a
transmitted component signal 1A be received directly, but that
somewhere along the propagation path a mechanism interacting with
the signal phase be encountered. Such an element can be a phase
lens or phase encoding mechanism. Element 2 performs this function.
The component signal 1A which propagates with known velocity
encounters the phase encoding mechanism 2 and is subsequently
received by the receiver 3. The received component signal 3A is
forwarded to the processing sequencer 4 and processing outputs are
sent on to the navigational information estimator 5.
The role of the phase encoding mechanism 2 is to encode in each
member signal information about one or more angular coordinates as
a phase distortion. Also, the phase distortion for each angular
coordinate must be unambiguously related to that coordinate.
Further, the phase distortion over the applicable frequency band
must be representable in good approximation by:
where, .theta..sub.o is a constant phase, .theta..sub.1 is a
complementary constant multiplying the angular frequency w.
The code for the angular coordinate is contained in the explicit
relation between the coordinate and G(w).
Property I as given earlier for the underlying base signals must be
substantially retained even after the action of the phase encoding
mechanism 2. Equation (3) should also be recognized as the first
two terms of a Taylor series expansion. Hence the character of this
approximation is based upon development of the received member
signal phase spectrum as a Taylor series with truncation of the
series after the second term. For the i.sup.th member signal of a
component signal, the following notation will be used:
to approximate the measured phase.
Phase encoding mechanisms of the type desired may be reflective in
nature as well as transmissive. A simple reflective encoding
mechanism which is described exactly by equation (3) is well known.
If the transmitted signal is reflected for some range of angles
which are all beyond the critical angle for the particular
reflective surface, a frequency independent phase encoding
.theta..sub.io is imposed which will vary with the particular
incidence angle. For this case .theta..sub.il will be identically
zero for all of the allowable incidence angles. See the discussion
"3-2: Reflection of a Pulse Incident Beyond the Critical Angle"
commencing on page 90 of Ewing, Jardetzky, and Press, Elastic Waves
in Layered Media, Lamont Geological Observatory contribution No.
189, McGraw-Hill, 1957 and also the work of Arons and Yennie, J.
Acoust. Soc. Amer., Vol. 22, pp. 231-237, 1950 for lucid accounts
of this phenomenon.
The navigational information for the generalized embodiment of FIG.
2 can be recovered by processing the received signal 3A through the
processing sequencer 4 which is shown in detail in FIG. 3. In FIG.
3 each member signal of the pattern within each component signal
must be identified and timed. The mathematical analysis of the
operational sequence is given in my above-referenced patent. Such
analysis describes how basic properties I through IV enable
individual member signals to be identified and correctly retain
arrival time and phase encoded angular coordinate information in
spite of appreciable distortions which may be present owing to
relative motion between the transmitter and receiver. Also, a
phase-invariant quadrature matched-filter processing sequencer
employing analogously design signals was described by Speiser and
Whitehouse at a symposium on Spread Spectrum Communications held at
the Naval Electronics Laboratory Center, San Diego, Mar. 13-16,
1973.
Member signals are identified for each of the significant peaks
detected by element 4F. Arrival times can be computed for each
member signal with the use of a time standard, however, signal
transmission times only can be determined if the signal initiation
times are known. The phases of the member signals can be computed
using the alternatives cited as elements 4G1 and 4G2. If the method
using arctangents of ratios of element 4G1 is elected, then if more
than a single member signal is involved, these must be in
quadrature. Again, the applicable analysis is given in my
above-referenced patent.
The navigational information estimator 5 of FIGS. 2 and 3 is
outlined in detail in FIG. 4. In both FIGS. 3 and 4, a subscript,
or the first subscript of a doubly subscripted quantity refers to
the number of an individual member signal of the pattern within a
component signal. Processing sequencer outputs 5A are both arrival
times t.sub.i for the member signals and phase functions. Since the
two term Taylor series expansion will be taken to approximate the
phase functions, these quantities will consist of either the
constant terms .theta..sub.io if the calculation of 4G1 is used, or
both .theta..sub.io and .theta.il, if the alternative 4G2 is
selected. The constants are complementary in that should the
.theta..sub.il not be determined as in the calculation of 4G1, they
will nevertheless be known by prior measurement or theoretical
calculation and so can be supplied by alternate means should this
be required.
Element 5C of FIG. 4 calculates member signal interval times. If
these interval times 5B1 are initially known, then in conjunction
with the signal propagation velocity V 5B5, radial relative
velocity components can be calculated according to element 5D.
Signal transmission times can be computed from the member signal
arrival times t.sub.i as in element 5E if member signal initiation
times 5B2 are known. Such transmission time is corrected as
indicated for phase terms linearly varying with frequency (elements
5B3, 5B4). Amongst such correction terms would be .theta..sub.il
which are either measured or complementary known terms as
previously discussed, and any linear phase terms of the
encodings.
Radial Range estimates between transmitter and receiver can be made
according to element 5F using any computed signal transmission
times T.sub.i (from element 5E) and the signal propagation
velocity. Provision is made in 5F for any known radial velocity
component as may have been previously determined by element 5D.
The decoding of the angular coordinates of element 5G is relatively
straightforward. First one corrects the measured constant phase for
any constants introduced by the base signals (element 5B7). Such
constants might result from the use of a pair of base signals
rotated in phase by a constant .chi. from base signals as defined
having symmetry and antisymmetry properties, respectively (Property
IV). Also, the base signals used in the processing sequencer 4 may
contribute constant phase modifications to the measured member
signal measured phases.
If a single angular coordinate is encoded in each member signal, we
need only associate the measured phase with the angular coordinate
via the known code. Where more than one angular coordinate is
encoded in each member signal, a somewhat more complex, but
simultaneous decoding scheme must be employed as described in the
echo location embodiment shown in FIG. 7 of my above-referenced
patent. In this case at least one angular coordinate must be
encoded differently in different member signals. Also, the codes
used must be independent and at least sufficient in number to
permit a simultaneous solution for the angular coordinates. If
there are redundant codes, a least squares solution can be
applied.
Since the case of more than one encoded angular coordinate may be
difficult to visualize, the following exemplary circumstance may be
considered. Assume that for two member signals which constitute a
component signal, the measured constant phases .theta..sub.oo and
.theta..sub.1o are determined. The two angular coordinates which
are encoded are .phi..sub.o and .phi..sub.1.
The constant phase encoding for .phi..sub.o will be taken as
.phi..sub.o /h.sub.o for both member signals, where h.sub.o is
taken as a known constant. For .phi..sub.1 on the other hand, the
encoding will be .phi..sub.1 /h.sub.1 for the first member signal
and .phi..sub.1 /h.sub.2 for the second one, where h.sub.1 and
h.sub.2 are known constants.
Now, the measurements .theta..sub.oo and .theta..sub.1o may be
related to .phi..sub.o .phi..sub.1, by the simply developed set of
equations: ##EQU2##
Simultaneous solution of equations (4) gives: ##EQU3## which is the
desired simultaneous decoding.
The embodiment of FIG. 2 was termed generalized for a variety of
reasons. First, it was not stated whether the receiver of the
transmitter was at the known location. Clearly, a navigation
application requires that one of these be known. Next, it was not
stated whether the component signal was sent off in response to
interrogation or at regular intervals. Further, it is implied that
the same or other transmitters can produce other component signals
concurrently, and that these can be received and processed in
analogous manner to give still other estimates of navigational
information.
Since viable navigation systems of this type (as described by FIG.
2) may operate according to any or all of the possibilities cited
above according to the principles already set forth, a more
concrete illustration of one alternative will help in the
visualization of the most general concept.
FIG. 5 shows an elementary area navigation system NS having a
single base station BS at a known location. Receivers 3 onboard
mobile platforms MP will be able to establish bearing angle .phi.,
radial range, and radial velocity with respect to this base
station.
The phase encoding of the bearing angle .phi. is established by
reflective means 2, the critical angle for the particular
reflective material being .beta..sub.c. A broad band source 1' of
pulsed electromagnetic radiation is required. Such a source might
be designed employing principles analogous to the Travitron
developed by Ikor, Inc., of Burlington, Massachusetts, which was
reported in the New Scientist, p. 285, Aug. 6, 1970.
Source 1' sends binary encoded pulse trains of member signals which
repeat on a five minute clock cycle that is precisely controlled.
The pulse sequences are sent at five second intervals according to
the code shown in FIG. 6. Note that the time of member signal
initiation can be determined by simple recognition of the binary
code. If a mobile platform remains stationary for several intervals
at a known location, sufficient information will be received to
calibrate a relatively low quality (and correspondingly
inexpensive) time standard. With such a calibration achieved, the
member signal initiation times are subsequently known.
Each of the component signal trains consists of no less than two
member signals, and each signal is of a nature previously described
(Properties I through IV). An appropriate frequency band in the
case of electromagnetic near shore navigation might be 100-500
mhz.
The system shown in FIGS. 5 and 6 thus requires no interrogation of
the transmitter and can provide redundant navigational information
by the conventional range-range approach, should there be
additional base stations. We can further recognize from this
exemplary case all of the essentials of the generalized embodiment
of FIG. 2. The processing sequencer of FIG. 3 and the navigational
information estimator of FIG. 4 are both specifically
applicable.
Alternative implementations of the generalized embodiment using
transmitter interrogations, or having known receiver locations and
mobile transmitters, or employing only the encoding of angular
coordinates will become readily apparent to those skilled in the
art.
Again, it is important to emphasize that methods employing phase
encoded angular coordinates may be used with conventional
approaches such as the range-range operation, where more than one
range determination may be made, and that standard statistical
procedures for combining and upgrading the accuracy of redundant
measurements may be employed.
It is useful at this point to relate features of the present
invention to the considerations presented in the background for the
invention. First, although member signals are pulse-like, they
still are of sufficient duration to benefit from correlation
detection, but also to suffer from Doppler distortions. Hence, a
phase invariant correlation and detection scheme which complements
the signal design is employed. If velocity information is desired
more than one member signal is required. While sequences of member
signals provide good redundancy and signal-to-noise ratio
advantage, their very duration limits the ability to resolve
changes in the relative velocity.
The defined class of signals have a remarkable ability to bear
angular coordinate information as a distortion-resistant phase
encoding. Several important practical advantages accrue to this
invention owing to this ability and two particularly sophisticated
extensions of the basic generalized embodiment of FIG. 2 will be
given below.
Certain practical matters should be first taken into consideration.
A rather standard approach to developing angular coordinate
information is to scan in the sense of the angular coordinate with
a narrow beam transmitter, as in the case of a conventional radar
system. Use of the narrow signal beam allows great concentration of
signal energy which has ensuing advantages in noisy environments.
On the negative side however, the time duration of the scanning
cycle may have portions of the navigation area without signal
coverage for unacceptable time periods.
The system of my invention is omnidirectional or at least broad
beam by nature. Any diminution of signal level accompanying this
feature may be overcome by frequent repetition of the signal
patterns over time and the development of statistical models
relating the information from one time to the next. In fact, the
work of R. E. Kalman as reported in the Journal of Basic
Engineering (ASME Transactions), Vol. 82, Pages 35-45, 1960, and
the subsequent work on Kalman filters by others offers an ideal
analytical vehicle to update the navigation information display 5H
of FIG. 4. My navigation system described herein would at no time
leave the navigation area without signal coverage for any
significant time period.
Also, the ability to label the signal transmission paths with
angular coordinates will solve an important problem occurring in
long range navigation systems using both electromagnetic and
acoustic signals. For electromagnetic signals the skywave or
ionospheric reflection sometimes may not be readily distinguished
from directly transmitted signals. Submarine navigation systems
similarly have multipath signal arrivals caused by reflections from
the acoustic impedance layering of the sea, which again may not be
conveniently distinguishable from direct transmission paths. If the
direct signal paths could be distinguished from secondary paths in
terms of an angular coordinate, then a new basis for identification
of the direct signal is developed.
It follows from the ability to label signal transmission paths with
angular coordinates, that a mobile unit such as shown in FIG. 5,
once positioned, may position other mobile units relative to itself
from their reflected signals or echoes. The transmitter and mobile
unit carrying the receiver being at known locations constitute an
echo location system.
Finally, one must consider the possibility that phase distortions
may be impressed into the member signals by properties of the
signal propagation medium itself. The presence of such distortions
may not necessarily be anticipated or even recognized.
An excellent case in point involves the use of water as a
propagation medium for acoustic signals centered around the
frequency 1.2 mhz. Such transmissions are often used as small scale
simulations of radar and microwave systems.
The following experimental study using the techniques of this
invention documents and measures the hitherto undetected phase
distortion or dispersive property of water at the cited
frequency.
In this study, the constant phase term, which will be taken to
characterize the phase effect of water as a dispersive transmission
medium, was sought for the frequency band 0.95-1.45 mhz (roughly
centered about 1.2 mhz). For the range of water transmission paths
between 2 and 7 cm in length, the constant phase distortion was
estimated to be 16.7.degree./cm. FIGS. 7, 8, 8a and 9 describe this
particular study.
FIG. 7 shows a schematic arrangement of the apparatus. A Datapulse
101 signal generator 1" was used to drive a transmitting transducer
1B which sends a narrow acoustic beam to a receiving transducer 3
through water W in an immersed open glass tube G. Signal generator
1" and transducer 3 were crystals having circular faces 1.905 cm
diameter, while the glass tube inner diameter measured 3.175 cm.
Received waveforms were recorded on Polaroid photographs from a
Tektronix type 561A oscilloscope 3A. The waveforms were
subsequently digitized at a sample interval of 0.122 .mu.sec using
a Wang calculator with an interfaced digitizer. The transmitted
waveform was in the nature of a member signal.
FIG. 8 shows plots of the digitized received member signal waveform
for propagation distances from 0 to 10 cm through the water. Owing
to the physical size of the transducer, only distances beyond 1.5
cm become representative of the far field signal transmissions.
Also, owing to the transducer beam width, results beyond 7.5 cm may
be expected to show tube sidewall interference effects.
In FIGS. 8 and 8a, and phase spectra are also shown for the
received member signals. The origins for the phase spectral
calculations are the time samples at or just before the member
signal origins as would be determined following the processing
sequence of FIG. 3. In this case, the correlation operations 4C1,
4C2 of FIG. 2 are performed with a Klauder signal base pair
occupying the frequency band of 0.89 to 1.48 mh.sub.z and the
origins selected are based on the peak times identified by element
4F. Hence the phase spectra and the identification of
characteristic constants over the significant frequency band
represent the operations of element 4G2. The simple behavior of the
phase spectra over the significant frequencies which results from
appropriate choice of the member signal origins will be
appreciated.
In FIG. 9 the detected constant phases as calculated from the phase
spectra over the band of significant frequencies (FIG. 8 and
element 4G2 of FIG. 3) are plotted against the propagation
distance, as are the constant phases computed according to element
4G1 of FIG. 3. The two calculations produce remarkably similar
results, which imply a simple linear relationship between the
constant phase distortion (imparted by the water) and the
propagation path length. As stated earlier, the slope of this
relationship is estimated to be 16.7.degree./cm of travel.
Hence, if signal phase distortions are present in the propagation
medium, as described, the following description will provide an
embodiment for a navigation system which can measure such
distortions and correct for them accordingly. The essentials for
this embodiment have much in common with the method employed to
encode more than one angular coordinate in a component signal.
For this embodiment the phase distortions imparted by the medium
are treated as one additional encoded angular coordinate. If
sufficient redundancy is designed into the component signal, and a
sufficient number of the encodings including the medium phase
distortion are mathematically independent, then the medium phase
distortion will be developed as a part of the same simultaneous
calculation for the angular coordinates. A specific illustration
will help clarify this general concept.
Assume that two member signals constitute the particular component
signal, and that the measured constant phases after processing
according to FIG. 3 are .theta..sub.oo and .theta..sub.10. The
single angular coordinate .phi..sub.o is phase encoded as
.phi..sub.o /.sub.ho in the first member signal and as .phi..sub.o
/h.sub.1 in the second one. A medium induced phase distortion
.phi..sub.m is present in both member signals which have travelled
over the same path.
The following equations relate the measurements 0.sub.oo and
0.sub.10 to the desired quantities .theta..sub.o and .theta..sub.m
: ##EQU4##
Solving equations (6) gives: ##EQU5##
If .phi..sub.m is calculated for many ranges, the phase distortion
of the medium can be rather simply characterized. Alternatively, if
.phi..sub.m is believed to relate to the range in a functionally
known manner and range estimates are available, then the decoding
equations can be reformulated to directly estimate the parameters
of the functional relationship.
In sum, navigation systems which embody elements of the invention
described herein offer several novel and highly desirable and
useful alternatives for addressing the compromises which inevitably
must be faced in developing area navigation systems.
* * * * *